The Polar Bear Game

“Polar Bears come in pairs.

They sit around a hole in the ice like petals on a flower.”

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To play: toss 5 dice and ask your friend how many creatures there are. For these directions, all six possible faces are shown. The dice with an asterisk are the ones used for that particular level.

Level 1: How many bears?

The story refers to a “hole in the ice.” The only dice that have these “holes” are 3 and 5. So, there are 2 bears on a die that shows three pips and 4 bears on a face that shows five pips. The arrangement on a face that shows six is not in “petal” form and doesn’t count.

Level 2: How many fish?

To count the fish, look into a “hole.” The opposite faces on a die have a sum of 7. There are 6 fish on a face with 1 pip, 4 fish when a 3 appears, and 2 fish when a 5 appears.

Level 3: How many plankton?

Fish eat plankton and fish are on faces that have “holes.” So, plankton hide on dice without holes. Plankton are small and appear in huge numbers in the sea. Find the sum of the even-numbered dice, multiply this sum by 7, and then add the number on the opposite face of the even dice.

Example:

There are 4 bears, 8 fish, and 105 plankton.

Which numbers should appear on the dice to give you the smallest number of

a.) bears?

b.) fish?

c.) plankton?

Which numbers should appear on the dice to give you the largest number of

a.) bears?

b.) fish?

c.) plankton?

Answer Key to page 2:

Toss #2

Which numbers should appear on the dice to give you the smallest number of

a.) bears?

b.) fish?

c.) plankton?

Which numbers should appear on the dice to give you the largest number of

a.) bears?

b.) fish?

c.) plankton?

					8 bears (from 3, 5, and 3) 10 fish (from 3, 5, and 3) 74 plankton [7*(6+4) + (1+3)]
			All fives (4 bears on 5 dice = 20 bears)
				All ones (6 fish on 5 dice = 30 fish)
				All sixes [(7*30) + 5 = 215 plankton)
				Any combination of 1, 2, 4, or 6 = no bears
				Any combination of 2, 4, or 6 = no fish
			Any combination of 1, 3, or 5 = no plankton